6 papers
Volume of quasi-homogeneous sublevel sets: Two linear algebra deterministic algorithms with convergence rates
Didier Henrion, Jean B Lasserre
We consider the problem of computing the Lebesgue volume of the unit sublevel set of a positive quasi-homogeneous polynomial. Pushing the Lebesgue measure of an ambient bounding bo…
Mixtures Closest to a Given Measure: A Semidefinite Programming Approach
SreÄko ÄuraÅ¡inoviÄ, Srećko Đurašinović, Jean-Bernard Lasserre +1
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settin…
A hierarchy of convex relaxations for the total variation distance
Jean-Bernard Lasserre
Given two measures , on Rd that satisfy Carleman's condition, we provide a numerical scheme to approximate as closely as desired the total variation distance between …
Verifying Properties of Binary Neural Networks Using Sparse Polynomial Optimization
Jianting Yang, SreÄko ÃuraÅ¡inoviÄ, Srećko Ðurašinović +3
This paper explores methods for verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Despite their lower computational and…
Leveraging Christoffel-Darboux Kernels to Strengthen Moment-SOS Relaxations
SreÄko ÃuraÅ¡inoviÄ, Perla Azzi, Jean-Bernard Lasserre +3
The classical Moment-Sum Of Squares hierarchy allows to approximate a global minimum of a polynomial optimization problem through semidefinite relaxations of increasing size. Howev…
Rank conditions for exactness of semidefinite relaxations in polynomial optimization
Jean B Lasserre
We consider the Moment-SOS hierarchy in polynomial optimization. We first provide a sufficient condition to solve the truncated K-moment problem associated with a given degree-…